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Concave function : ウィキペディア英語版
Concave function

In mathematics, a concave function is the negative of a convex function. A concave function is also synonymously called concave downwards, concave down, convex upwards, convex cap or upper convex.
==Definition==
A real-valued function on an interval (or, more generally, a convex set in vector space) is said to be ''concave'' if, for any and in the interval and for any in (),
:f((1-t)x+(t)y)\geq (1-t) f(x)+(t)f(y).
A function is called ''strictly concave'' if
:f((1-t)x + (t)y) > (1-t) f(x) + (t)f(y)\,
for any in (0,1) and .
For a function , this definition merely states that for every between and , the point on the graph of is above the straight line joining the points and .
A function is quasiconcave if the upper contour sets of the function S(a)=\ are convex sets.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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